Preheat oven to 375 degrees. Mix together flour, ginger, allspice & baking sode. Cream together sugar, applesauce and molasses. Add dry ingredients to wet and stir just until combined. Pur extra sugar inot a saucer or shallow dish. Roll dough into balls, a tablespoon at a time, then roll in sugar and place on sprayed/greased cookie sheet, flattening slightly. Bake 6 to 8 minutes for chewy cookies, 12 to 15 minutes to crispy.